WEBVTT 00:00:00.000 --> 00:00:02.840 This is College Physics Answers with Shaun Dychko. 00:00:03.900 --> 00:00:06.640 An Olympic runner who starts a race with an acceleration of 00:00:06.640 --> 00:00:08.640 4.5 meters per second squared. 00:00:08.900 --> 00:00:12.920 Since they are starting the race, we can assume that their initial velocity, 00:00:12.920 --> 00:00:14.580 which I guess we call v naught , 00:00:14.640 --> 00:00:15.920 is zero 00:00:16.000 --> 00:00:19.680 and they are gonna be racing for 2.40 seconds. 00:00:20.560 --> 00:00:23.460 Part (a) asks us for the final speed 00:00:23.560 --> 00:00:26.660 so that will be the initial speed plus acceleration times time— 00:00:26.660 --> 00:00:28.980 that's equation 52 in chapter 2— 00:00:29.160 --> 00:00:31.520 and so that's 0 meters per second to start with 00:00:31.520 --> 00:00:34.460 plus 4.5 meters per second squared acceleration 00:00:34.460 --> 00:00:36.320 multiplied by 2.4 seconds 00:00:36.320 --> 00:00:39.480 giving 10.8 meters per second will be their final speed. 00:00:40.580 --> 00:00:43.820 And then to sketch a graph of their position vs. time, 00:00:43.900 --> 00:00:47.440 I used a spreadsheet program called the LibreOffice 00:00:47.440 --> 00:00:50.280 which is like a free version of Excel 00:00:51.600 --> 00:00:53.000 and it's here 00:00:53.040 --> 00:00:56.120 and I have put in some time's from 0, 00:00:56.360 --> 00:00:58.940 0.5 second, 1 second, 1.5 seconds and so on 00:00:59.020 --> 00:01:03.780 and then the position is this equation which I'll explain over here; 00:01:05.580 --> 00:01:10.360 we have equation 53 in chapter 2 says that the final position 00:01:10.360 --> 00:01:14.320 is the initial position plus initial speed times time 00:01:14.320 --> 00:01:17.400 plus one-half times acceleration times time squared 00:01:17.520 --> 00:01:21.340 and in this case, they start at position 0 so that's 0. 00:01:21.340 --> 00:01:25.060 They start at rest so the v naught is 0 00:01:25.180 --> 00:01:28.640 and so we have the acceleration of 4.5 meters per second squared 00:01:28.640 --> 00:01:32.040 multiplied by this half from the formula times t squared 00:01:32.040 --> 00:01:35.220 that's the formula that is here 00:01:35.220 --> 00:01:41.280 written as 0.5 times 4.5 multiplied by cell A3, 00:01:41.280 --> 00:01:44.360 which is the cell right beside where we are 00:01:44.360 --> 00:01:47.320 in column A at the same row 00:01:47.400 --> 00:01:50.480 and that's squared so that's this caret symbol which is 00:01:50.480 --> 00:01:56.880 'Shift plus 6' and then the number 2 to say that it is to the power of 2. 00:01:57.320 --> 00:02:03.260 So this is one-half times 4.5 times time squared—that's the position. 00:02:03.320 --> 00:02:06.400 And then we made this chart; time on the horizontal axis, 00:02:06.400 --> 00:02:07.600 position on the vertical axis 00:02:07.600 --> 00:02:10.680 and we have the units of meters for position and seconds for time. 00:02:10.860 --> 00:02:15.600 And then I inserted a trend line to extrapolate between the points 00:02:16.060 --> 00:02:18.380 and then there we go 00:02:18.380 --> 00:02:21.340 that's the graph that's copied here 00:02:22.040 --> 00:02:23.980 and it has this equation.